of Newton's Rings. 411 



of the second medium, and will partially enter the first medium : 

 >ts phase will be ^(vt- x) - 2V , and so for succeeding reflexions 



Now suppose that at the last surface of the first medium, the 

 coerhc.ent of the incident vibration being 1, that of the reflected 

 v.bratmn is e and that of the refracted /; at the first surface of 

 the second medium, suppose the coefficient of the reflected vi- 

 bration to be g; and for light incident from air on the surface of 

 the first medium, suppose the coefficients of the reflected and 

 retracted vibrations to be h and A. Then, the coefficient in the 

 incident light being a, 



That in the first reflected light is ae 



that in the refracted light is af 



that in the light reflected at the second medium is afg 

 and that in the light refracted into the first medium is afgh 



that in the light reflected from the first medium is afgh 



that in the light reflected from the second medium is afgh 



and that in the light refracted into the first medium is afg*hk 



and so on; the coefficients after the first following a geometrical 

 progression whose ratio is gh. Thus it appears that the whole 

 vibration will be 



%■*, ^{^-{vt-x)-r)-gh.sm{^{vt-x)\ 

 or a.e.sm--(vt-x) + a.fg/c. Li ' \ * ' ) 



l-Zgh.cosf+g'h' • 



Now in Fresnel's expressions, 



_ tan (t - 1) 

 tan (« + .') ' 

 Vol. IV. Part III. 3G 



